A random variable let say X is taken as a function whose domain is the S i.e. sample space, and then the range is being set.

A sample space consisting of discrete elements then the r. is known as the discrete r.v. If the sample space consists of uninterrupted elements, then it is called as continuous r.v. The probability distribution is the distribution of the random variables. On the other hand, regarding r.v., the probability distribution is called as the discrete distribution or the continuous distribution. Thus the discrete distribution is thus represented by probability mass function given below:

x | -1 | 0 | 1 |

p(x) | 0.2 | 0.4 | 0.4 |

Thus it is a discrete distribution. Here, the variable X contains values like -1, 0 and 1 with probability 0.2, 0.4 and 0.4 respectively.

So, the characteristic of *pmf* or the probable mass function are as follows:

- P(x) 2: 0 for all x
- Σ p(x) = 1

Any continuous distribution is represented by probability density function or *pdf. *Let’s consider an example,

f(x) = 1, 0<x<1=0

Here the random variable can take any value between 0 and 1 with probability 1, and 0 for any other value.

Therefore the characteristic of *pdf* is:

- F(x) ≥ 0 for all x
^{∞}ʃ_{-∞ }f(x) dx = 1

**Links of Previous Main Topic:-**

- Introduction to statistics
- Knowledge of central tendency or location
- Definition of dispersion
- Moments
- Bivariate distribution
- Theorem of total probability addition theorem

**Links of Next Statistics Topics:-**

- Binomial distribution
- What is sampling
- Estimation
- Statistical hypothesis and related terms
- Analysis of variance introduction
- Definition of stochastic process
- Introduction operations research
- Introduction and mathematical formulation in transportation problems
- Introduction and mathematical formulation
- Queuing theory introduction
- Inventory control introduction
- Simulation introduction
- Time calculations in network
- Introduction of game theory